1. Field of the Invention
The present invention relates to a diffraction grating device having a refractive index modulation formed in an optical waveguide region in a predetermined region in the longitudinal direction of an optical waveguide.
2. Related Background Art
A diffraction grating device has a refractive index modulation formed in an optical waveguide region (at least a core region) in a predetermined region in the longitudinal direction of an optical waveguide (optical fiber or planar optical waveguide). Such a diffraction grating device can selectively diffract and reflect light having a wavelength corresponding to the period of the refractive index modulation and is used as an optical filer or the like. In this diffraction grating device, preferably, the reflectance is constant in the reflection wavelength band, the reflectance is almost zero in the transmission wavelength band, and the reflectance abruptly changes near the boundary between the reflection wavelength band and the transmission wavelength band. That is, the reflection spectrum of the diffraction grating device is preferably almost rectangular as much as possible.
Generally, when the reflectance in the reflection wavelength band is almost 100%, even a diffraction grating device having a normal refractive index modulation with a uniform optical period (=average refractive indexxc3x97period) and uniform amplitude can have a reflection spectrum close to a rectangle. However, when the reflectance in the reflection wavelength band is low, the reflection spectrum of a diffraction grating device indicates no constant reflectance but a reflectance represented by a quadratic function in the reflection wavelength band. A diffraction grating device that aims at obtaining a constant reflectance even when the reflectance in the reflection wavelength band is low has been proposed.
For example, a diffraction grating device described in reference 1 xe2x80x9cJapanese Patent Laid-Open No. 9-222522xe2x80x9d aims at obtaining a constant reflectance even at a low reflectance in the reflection wavelength band by defining as a sinc function an envelope representing the amplitude distribution of the refractive index modulation in the longitudinal direction and by inverting the phase of the refractive index modulation at the phase inversion portion. A diffraction grating device described in reference 2 xe2x80x9cS. Bonino, et al., xe2x80x9cSpectral Behavior Analysis of Chirped Fibre Bragg Gratings for Optical Dispersion Compensationxe2x80x9d, ECOC ""97 (1997)xe2x80x9d aims at obtaining a constant reflectance even at a low reflectance in the reflection wavelength band by defining as a tanh function a refractive index modulation amplitude distribution and by changing the period of the refractive index modulation in the longitudinal direction.
The present inventors examined the prior arts and found the following problem. For the diffraction grating device described in reference 1, let L be the optical distance (=average refractive indexxc3x97geometrical distance) between two adjacent phase inversion portions, and xcexB be the central diffraction wavelength. On the basis of the coupled wave theory, a bandwidth xcex94xcex of the reflection spectrum is approximately given by
xcex94xcex=xcexB2/2LSxe2x80x83xe2x80x83(6)
For example, when xcex94xcex=0.2 nm and xcexB=1.55 xcexcm, LS=6.0 mm. To make the reflection spectrum closer to a rectangular shape, the length of the region where the refractive index modulation is formed must be increased. For example, when the length of the region where the refravtive index modulation is formed is 20LS, the optical distance is as long as 120 mm. In the diffraction grating device described in reference 2, when the bandwidth xcex94xcex of the reflection spectrum is 0.4 nm, the length of the region where the refractive index modulation is formed is as long as 100 mm. As described above, in the diffraction grating devices described in references 1 and 2, the region where the refractive index modulation is formed inevitably becomes long.
To maintain a constant reflection spectrum for a diffraction grating device, the temperature of the diffraction grating device must be kept constant using a Peltier device or the like, or temperature compensation must be done by applying a tension to the diffraction grating device using a member having a thermal expansion coefficient different from that of the diffraction grating device. However, when the region where the refractive index modulation is formed is long, assembly for temperature adjustment or tension application is difficult, and the reflection spectrum of the diffraction grating device can hardly be kept constant when the temperature varies.
The diffraction grating device described in reference 1 aims at obtaining a constant reflectance even at a low reflectance in the reflection wavelength band. However, even when the length of the region where the refractive index modulation is formed is set to 20LS, the deviation in reflectance in the reflection wavelength band is as large as about 20%.
The present invention has been made to solve the above problems, and has as its object to provide a diffraction grating device which can shorten the region where the refractive index modulation is formed, and flatten the reflectance characteristic in the reflection wavelength band.
A diffraction grating device according to the present invention is a diffraction grating device having a refractive index modulation formed in an optical waveguide region in a predetermined region in a longitudinal direction of an optical waveguide. In this diffraction grating device, the optical period of the refractive index modulation is substantially constant, the phase of the refractive index modulation is inverted at a phase inversion portion, and the number of phase inversion portions present in the predetermined region is one or two. When z is a variable representing a position in the longitudinal direction using a barycentric position of the predetermined region as an origin, that is, z is an optical distance from the origin, xcex94n(z) is the amplitude distribution of the refractive index modulation, and the sign of the amplitude distribution xcex94n(z) is changed at the phase inversion portion, parameters A0, A2, B0, and B2 obtained by integral calculations in the predetermined region are given by
A0=∫xcex94n(z)dzxe2x80x83xe2x80x83(7a)
A2=∫z2xc2x7xcex94n(z)dzxe2x80x83xe2x80x83(7b)
B0=∫|xcex94n(z)|dzxe2x80x83xe2x80x83(7c)
B2=∫z2xc2x7|xcex94n(z)|dzxe2x80x83xe2x80x83(7d)
and for the parameters A0, A2, B0, and B2, a condition given by                               "LeftBracketingBar"                                                    A                2                            ·                              B                0                                                                    A                0                            ·                              B                2                                              "RightBracketingBar"                 less than         0.25                            (        8        )            
holds.
The diffraction grating device according to the present invention, which satisfies the above conditions, can shorten the region where the refractive index modulation is formed and flatten the reflectance characteristic in the reflection wavelength band. Hence, in this diffraction grating device, assembly for temperature adjustment or tension application is easy, and the reflection spectrum of the diffraction grating device can easily be kept constant when the temperature varies.
The diffraction grating device according to the present invention may be characterized in that the amplitude distribution xcex94n(z) of the refractive index modulation is 0 at the phase inversion portion. In this case, the side lobe in the transmission wavelength band can be reduced while maintaining the flat reflectance characterisitic in the reflection wavelength band.
The diffraction grating device according to the present invention may be characterized in that an average refractive index is constant in the predetermined region, and the amplitude distribution xcex94n(z) of the refractive index modulation is represented by a cos function. In this case, the diffraction grating device can easily be manufactured using two types of normal phase grating masks each having a periodically three-dimensional surface.
A diffraction grating device according to the present invention is a diffraction grating device having a refractive index modulation formed in an optical waveguide region in a predetermined region in a longitudinal direction of an optical waveguide. When z is a variable representing a position in the longitudinal direction using a central position of the predetermined region as an origin, that is, z is an optical distance from the origin, xcex94n(z) is the amplitude distribution of the refractive index modulation, and xcex4xcex8(z) is the phase shift distribution of the refractive index modulation with reference to a period defined from a central diffraction wavelength, the amplitude distribution xcex94n(z) of the refractive index modulation is represented by an even function, the phase shift distribution xcex4xcex8(z) of the refractive index modulation is represented by an even and continuous function, and parameters A0C, A0S, A2C, A2S, B0, and B2 obtained by integral calculations in the predetermined region are given by
A0C=∫xcex94n(z)xc2x7cos(xcex4xcex8(z))dzxe2x80x83xe2x80x83(9a)
A0S=∫xcex94n(z)xc2x7sin(xcex4xcex8(z))dzxe2x80x83xe2x80x83(9b)
A2C=∫z2xc2x7xcex94n(z)xc2x7cos(xcex4xcex8z))dzxe2x80x83xe2x80x83(9c)
A2S=∫z2xc2x7xcex94n(z)xc2x7sin(xcex4xcex8(z))dzxe2x80x83xe2x80x83(9d)
B0∫xcex94n(z)dzxe2x80x83xe2x80x83(9e)
B2=∫z2xc2x7xcex94n(z)dzxe2x80x83xe2x80x83(9f)
for the parameters A0C, A0S, A2C, A2S, B0, and B2, a condition given by                               "LeftBracketingBar"                                                    (                                                                            A                                              0                        ⁢                        c                                                              ·                                          A                                              2                        ⁢                        c                                                                              +                                                            A                                              0                        ⁢                        s                                                              ·                                          A                                              2                        ⁢                        s                                                                                            )                            ·                              B                0                                                                    (                                                      A                                          0                      ⁢                      c                                        2                                    +                                      A                                          0                      ⁢                      s                                        2                                                  )                            ·                              B                2                                              "RightBracketingBar"                 less than         0.25                            (        10        )            
holds, and a condition given by
|xcex4xcex8(z)xe2x88x92xcex4xcex8(0)| less than 2xcfx80xe2x80x83xe2x80x83(11)
holds in the predetermined region.
The diffraction grating device according to the present invention, which satisfies the above conditions, can also shorten the region where the refractive index modulation is formed and flatten the reflectance characteristic in the reflection wavelength band. Hence, in this diffraction grating device, assembly for temperature adjustment or tension application is easy, and the reflection spectrum of the diffraction grating device can easily be kept constant when the temperature varies.
The diffraction grating device according to the present invention may be characterized in that the amplitude distribution xcex94n(z) of the refractive index modulation has two minimal points of absolute value in the predetermined region. In this case, the change in reflectance can be made steep near the boundary between the reflection wavelength band and the transmission wavelength band.
The present invention can be readily understood from the following detailed description taken in conjunction with the accompanying drawings. These drawings are merely examples and do not limit the present invention.